An open invoice is one that can still be edited in terms of amounts, type of payment and others. These do not appear in the quarter summary nor do they transfer to the 480's. It can be said that it is an invoice that has not been paid.
The registered invoice blocks the fields so that it cannot be altered. The amounts reported in this type of invoice do appear in the summary of the quarter and are transferred to the 480's. If you wanted to update or correct any information, you would have to unregister the invoice.
A void invoice is one whose information is saved, but it will not be reflected in reports, summaries or transferred to the informative.